The Jam Tarts have now gone four games without a goal and have slipped down the table as a result.
It was the home side who made the best possible start by taking the lead in only the 11th minute.
Hearts signing target Chris Porter's header ended an excellent passing move involving Jim O'Brien, Paul Quinn and Stephen Hughes.
It took Hearts until the 32nd minute to have any kind of effort at goal but all Christian Nade could do was power a header over.
The first half was spoiled as a spectacle by an over-fussy referee who blew for free-kicks far too often rather than let the game flow.
With the first half having little to commend it the fans had a right to expect better in the second. Sadly the opening stages were little better with the only effort of note coming from Eggert Jonsson whose shot from 20 yards was easy for 'Well keeper Graeme Smith.
In an effort to solve their goal drought Hearts boss Csaba Laszlo replaced Nade with Calum Elliot who had bagged 14 goals in a recently ended loan spell at Livingston.
Motherwell seemed content to soak up anything Hearts could throw at them while looking dangerous on the break. It was only the desire to take an extra touch that prevented them adding to their lead.
In the end they held on comfortably enough for three points which drags them back into the race for a top six slot.